Well Well Well (user has been chat banned--call of duty joke for the kids)
Looks like someone stayed at a Holiday In Express and then tried to do stats. Let's just say you would not be faring very well in my class.
For shooting purposes which "formula" you use (I'll get to the quotes shortly) is largely irrelevant unless you like Math Bitch Fights(TM)
Luckily I do.
Let's go to the tape:
0:20 or so "Comparing it to the Labradar..." (Uh oh! You used the magic words!)
0:36 "I collected more data" (aka Darth Vader: 'I have altered the deal' To do a proper statistical test the sameple sizes are fixed beforehand so you can estimate the statistical power of your test. Big Red Flag(TM) on your 'testing'
0:50 "Whether the ejector made any Difference, It Didn't" Data?
1:23 "Labradar and Garmin were similar" In statistics there is no similar, either their performance is the same or not. Its a Yes/No test. Typically we are asked to provide test statistics the standard of which are described
here 1:34 "5 shot Velocity Average were about the same" Again, its a yes/no test. "About" is a weasal word in statistics and SHOULD NOT BE USED.
1:33 "It [Labradar] uses the wrong equation....Should not be using an inferential statistical equation" You were correct in that it uses a different equation. However, it is not wrong. And here starts the heart of your Hubris.
σ or Standard Deviation is an Intrinsic Property. If I take 5 shots and measure standard deviation, that is the property of that data. However, that's not what most people are trying to find. They are trying to measure the standard deviation. As a bonifide math geek I am sure you are familiar with Jensen's Inequality which states that an estimate of the value of a concave function is ALWAYS less than or equal to the actual value. In layman's terms for those playing along, this means that if you try to measure σ, that value is TOO SMALL or BIASED towards the actual measured data. Thus if you want to estimate the distrubution of you MV you should use s or "estimated σ". Of course these differ only by a factor of sqrt(N/(N-1)) but it is measurable, especially with very small sample size (like 5).
1:53 "A gross misapplication"
Actually it is the proper statistic to apply in your very stated case (see first comment) of comparing Labradar Performance to Garmin or doing a test to compare ejector effect. Both of these are comparing two processes and thus fall under 7.3.1 of the NIST standards shown above and standard in any statistics handbook or text. You statement is demonstrably FALSE
1:55 "Certain Type os Standard Deviation" There is std dev and estimated std dev. They are not types, one is the intrinsic value of a dataset (in this case all shots ever fired under specific conditions) the other is a estimate or measure (which is know is biased, so we correct for it) of that value.
2:05 "Garmin uses the correct equation" Depend on what you are doing. If you are trying to get a basedline, the Garmin is correct. If you are comparing things (as you are, or say doing a ladder test) then the LabRadar method is the statistically correct method. As mentioned by other uses, the difference is largely negligible escially as N becomes large, but when making claims of "Gross Misapplication" I would thing details like this DO matter.
2:18 "Extreme Spreads were a little bit different" As a statistician, the min max values have no statistical bearing on the distribution. While they contribute to the distribution, as a reminder the Guamanian or normal distribution has 2 independent parameters σ and μ, which are the only two which characterize the distribution. In essence you are saying "the std dev is different" as those values contribute to both the mean (or estimated mean) and std.dev (or estimated std.dev). You also fail to quantify "little" Statistics is math. Amounts should be quantified. To compare the ES a 1-sided t-test would be appropriate
2:37 "Little bit of Variability" No. It is a machine to machine difference that can be measured and quantified.
2:45 I just realized that your 22 shots are in fact 14 and 8 shots The last 8 shots are clearly 200FPS less (and you stated that you changed the process) so your SD is in fact over 2 separate processes. This is a huge no-no--you kniwing changed processes and include your n=22 and talk about the "process" when in fact you cannot do a head to head comparison but must do an ANOVA test to account for the multiple variables (Ejector condition, Equipment Condition, Cartridge Condition). This is a gross misapplication of statistics. It demonstrates that you have 0 knowledge or understanding of home to properly apply statistics. It negates your ES test 100% as you failed to account for the process change at shot 15 and violates a basic rule of analysis. Especially as that change in MV inflates your SD (pick a method) and allows to to claim they are the same (This is a Lies, Damn Lies, Statistics type failure)
3:11 "All those [6PPC 30BR] combined" STATISTICS FAIL!! You cannot combine those to produce a means. Nope. Nada. Fail
3:20 "The Labradar has an inflated standard deviation..not apporpriate" Indeed that is the point. Pull a total Obi-Wan, from a certain point of view, you are correct: The Labradar Std.Dev is inflated. The reason of course is because the Std.Dev produced by the Garmin is BIASED or too low for this type of process comparison. The correct method to estimate the std.dev or s is being used by Lab Radar strictly speaking. It is "inflated" because a measurement useing the "true" formula is TOO LOW and has been mathematical PROVED (Jensen's Inequality). So it is in actuallity MORE appropriate. Ooooo so close.
3:42 "Not significantly differnt" Well yeah because you FUBAR'd the data collection beyond recognition and introduced unaccounted for factors like switching rounds in the middle of the test.
3:50 "If you shot in 10 to 20 more times i t would become statistically significant" CHALLENGE ISSUED. I bet a new AXSR that if this test is repeated 10 times there would be NO STATISTICAL DIFFERENCE BETWEEN THE LABRADAR AND GARMIN. That's how full of BS your case is. Repeat this same test. 10 times. (14 shots , 8 shots x10 labradar vs garmin in for ES--even as a bullshit metric I can tell you the result right now) It will not be different. I 100% guarantee it and am willing to place a bet worth 1 AXSR in 338 Lapua New from Mile High. I'll send you my FFL info. (and i even swore off AI)
4:25 "I am getting the same" No I accept the null hypothesis that the distributions are the same (even though you totally fucked up(tm) the analysis)
NOW GET THIS WEAK SHIT OUTTA HERE BEFORE I BUST OUT MY RED PEN.
Sorry my spelling is shit. That's why I went into math and science.
TLDR for the short attention span:
Brian doesn't know his ass from a hole in the ground when it comes to stats. He uses a lot of weasal words and statistical terms out of context to sound smart, but is acutally just full of it.
While it really doesn't matter, strictly speaking the Labradar (estimated std dev of STDEV.S) is the correct metric.
Brian failed to account for the change in cartridge, which inflated his Std Dev allowing him to make unsubstatiated claims about process similarities. AKA he fucked up the test. Badly. He also made an outrageous claim about statistical significance so I called BS
www.snipershide.com 
